The Pythagorean Theorem

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Presentation transcript:

The Pythagorean Theorem Chapter 9.1 Part 2

The Converse of the Pythagorean Theorem: In a triangle with sides a, b, and c; if , then the triangle is a right triangle. Are the following right triangles? 1. a = 9, b = 12, c = 15 2. a = 1, b = 2, c = 3 False. Not a right triangle. True. Yes it is a right triangle.

In your Notebooks: Is this a right triangle? SHOW YOUR WORK! 4, 5, 6 2) 8, 15, 17 3) 20, 21, 29 4) 3, 8, 15 We will continue taking notes in 5-10 minutes.

Word Problems: Suppose that you drive 4 miles south and then 10 miles east. How far are you away from your starting point? Step 1: Draw a picture: 4 miles 10 miles

Word Problems: Suppose that you drive 4 miles south and then 10 miles east. How far are you away from your starting point? Step 2: Set up and equation, and solve. Distance from starting point 4 miles 10 miles miles

Applications of the Pythagorean Theorem: Use your own paper. You may work in groups of 2-3. Passing the AIMS: pg 253, 1-4 all Create your own word problem using distances, and solve using the Pythagorean theorem. For example: Bob walked 6 miles north, turned and walked 8 miles west. How far away is he from his original position? Keep your papers

Pythagorean Triples: All three sides of a right triangle are positive integers. Which of the following are Pythagorean triples. Justify your answers (use converse of Pythagorean Theorem.) 30 , 40 , 50 2) 14, 48, 50 3) 12, 35, 37 4) 48, 55, 73 5) 36, 77, 85 6) 16, 30, 34 7) 9, 40, 41 8) 11, 60, 61

Hint: look for GCF and Factor 9) What do the following triples have in common? 10) Which ones are the sides of a right triangle? 3, 4, 5 6, 8, 10 9, 12, 15 12, 16, 20 15, 20, 25 30, 40, 50 Hint: look for GCF and Factor

Homework: pg 417 (18, 21-32 all, 37) SHOW YOUR WORK! For Converse of Pythagorean Theorem: EXPLAIN YOUR ANSWERS SHOW YOUR WORK!